。
She is constantly plagued by neuralgia.
Literal
She [topic-は] ceaselessly neuralgia [by-に] is-being-troubled.
絶えず (たえず) means 'constantly' or 'ceaselessly' — from 絶える (to cease) + the classical negative ず, literally 'without ceasing.' 神経痛 (しんけいつう) means 'neuralgia,' a medical compound of 神経 (nerve) + 痛 (pain). 悩まされている is the passive of 悩ます (to trouble, to afflict), putting her as the person being affected — an adversative passive where the illness is the unwelcome agent. The combination of 絶えず with ~ている emphasizes the relentless, chronic nature of her suffering.